Import .obj with vertices' UV specified into Cycles?
When you imported the .obj file, it should have also imported the UV Map that was stored within it. You can verify this under the mesh tab of the properties panel. With the object selected, go to the properties panel (bottom right by default) and click on the mesh tab (looks like a triangle made up of three dots joined by lines).

If you scroll down to UV Maps, you can see all UV Maps applicable to your object. If you have just imported your object and done nothing else, you should see one entry, being the UV Map that you imported along with your object.

Cycles will use that UV Map by default for any image texture in any material that you assign to the object. If you have more than one UV Map on an object you can select the relevant UV Map using the UV Map node, but you should not need to do this unless you have created a second UV Map.